Plymouth Rock Securities is interested in finding out if there is a relationship between the number of new clients brought into the firm by a broker and the sales performance of the broker. A random sample of 11 brokers' records are reviewed to determine the number of new clients enrolled last year and total sales in millions of dollars: (12pts)

Question

Broker

1

2

3

4

5

6

7

8

9

10

11


Clients

27

11

42

33

15

15

25

36

28

30

17


Sales, $

52

37

64

55

29

34

58

59

44

48

31




a) How closely related is the new client base to sales performance? Draw the scatterplot and compute the correlation and describe the relationship

b) Find the least-squares equation to predict sales from number of clients. Can the least squares equation be used to predict sales?

c) What does the slope represent?

d) What would a new broker who brings in 30 clients sell, on average?

e) How much of the variability in sales is not explained by the number of new clients